This multicenter Phase I/II study is divided into two parts. Part A will determine the safety, tolerance and pharmacokinetics of the combination of ddI with ZDV in HIV-infected infants or exposed infants on ZDV < 120 days of age. Part B will be a Phase II evaluation of ddI alone versus ddI/ZDV in HIV-infected infants enrolled < 90 days of age. The study is designed in two parts to optimally obtain both Phase I and Phase II data for this select group of subjects.